Development of fast methods to conduct in silico experiments using computational models of cellular signaling is a promising approach toward advances in personalized medicine. However, software-based cellular network simulation has run-times plagued by wasted CPU cycles and unnecessary processes. Hardware-based simulation affords substantial speedup, but prior attempts at hardware-based biological simulation have been limited in scope and have suffered from inaccuracies due to poor random number generation. In this work, we propose several hardware-based simulation schemes utilizing novel random update index generation techniques for step-based and round-based stochastic simulations of cellular networks. Our results show improved runtimes while maintaining simulation accuracy compared to software implementations.